Fractal Domain

Fractal domain is a function domain D, where D is a fractal set. As there is no clear definition of a fractal, except for the ones most "popular" (such as that the fractal set is any set that has the non-integer Hausdorff dimension), not much more can be said here. A function with a fractal domain is, for example, Hausdorff dimension itself. We lay \dim_H(D)=d, where d\in (0,\infty). Therefore we have d\colon D \mapsto (0,\infty).

 

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